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180                              CHEMICAL ENGINEERING
fan blowers do there seem to be occasionally some serious discrepancies near the point of maximum efficiency.1
Multi-stage Centrifugal Compressors.—A multi-stage compressor consists of a number of single-stage compressors connected in series. When the number of single-stage compressors is small they are usually enclosed in the same casing; but when the number exceeds eight or ten they are generally subdivided between two or more casings, separated by intercoolers. Multi-stage compressors are frequently built with single-inlet impellers, depending for the overcoming of the axial thrust on balancing pistons, on special grouping of the impellers, and on similar devices; also with backward-discharge impellers, when they are supplied with substantial shrouds to prevent the blades from bending or breaking under the action of centrifugal force. They are also built with all the impellers of the double-inlet type, thus obviating the need of all balancing means and
i Numerical Examples. Power Required.—Find the power required to compress adiabatically 20,000 cu. ft. of air per minute from atmosphere to 30 Ib. per square inch gage, the shaft efficiency of the compressor being 75 per cent.
Solution.—From Table 14, p. 177, the theoretical horsepower is 8.4 X 20,000/100 = 1,680, and the shaft horsepower is 1,680/0.75 = 2,240.
Equivalent Suction Pressure.—What suction can be obtained with a compressor rated to deliver 2,500 cu. ft. of air per minute against 2 Ib. per square inch gage?
Solution.—The compressor is rated for an initial pressure of 14.7 Ib. per square inch. Since the pressure ratio depends only on the wheel speed, the hydraulic efficiency and the initial temperature, all of which are supposed to remain the same, the initial suction pressure is (14.7/16.7) X 14.7 = 12.94 Ib. per sauare inch absolute, and the suction obtained is 14.70 — 12.94 = 1.76 Ib. per square inch.
Equivalent Pressure when Compressing Gas.—What pressure can be obtained when compressing water gas with a standard unit rated 25,000 cu. ft. of air per minute and 15 Ib. per square inch gage, and what power will be required if it requires 2,000 horsepower to compress the air to 15 Ib. pressure?
Solution.—The density of water gas is 0.05167, and its specific gravity (compared with air) is 0.677. The mean effective pressure (m.e.p.) corresponding to 15 Ib, per square inch is 11.44 for air (see also Table 1). For water gas, everything remaining the same, m.e.p. = 11.44 X 0.677 = 7.74 Ib. per square inch, and from Table 1 the corresponding final pressure is 9.3 Ib. per square inch gage. The theoretical power for the air rating (from Table 2) is 5 X 25,000/100 = 1,250 horsepower. For water gas the theoretical horsepower is 1,250 X 0.677 = 846 hp., and the actual power = 2,000 X 0.677 = l,354hp.
Equivalent Rating at Other Speeds.—A standard centrifugal compressor rated 4,500 cu. ft. of air and 15 Ib. per square inch pressure is to be speeded up from 3,450 r.p.m. to 4,000 r.p.m. What increase of pressure and of quantity will result?
Solution.—The mean effective pressure for 15 Ib. per sauare inch is 11.44. At 4,000 r.p.rn. it will increase to (4,000/3,450)- X 11.44 = 15.38, and the corresponding final pressure from Table 1 is 22.05 Ib. per square inch absolute. Also the new quantity will be (4,000/3,450) X 4,500 = 5,220 cubic feet per minute if the same ratio of va/va, and therefore the same hydraulic efficiency, is to be maintained (see "Quantity Constant" and "Load Coefficient," page 178).
General Problem.—What standard compressor can be used to exhaust 18,500 cu. ft. of anthracite producer gas per minute against a suction of 7 Ib. per square inch? The compressor is to be installed 2,000 ft. above sea level. What horsepower is required?
Solution.—The barometer at 2,000 ft. altitude is 13.56. The compressor is therefore required to compress the gas from 13.56 - 7.00 = 6.56 Ib. per square inch absolute to 13.56 Ib. This is equivalent to compressing the gas at sea level to a final pressure of (13.56/6.56 ) X 14.7 = 30.4 Ib. per square inch absolute or 15.7 Ib. gage. The density of anthracite producer gas is 0.065 Ib. per cubic feet. The mean effective pressure corresponding to 15.7 final pressure is (/Table 1) 11.9 Ib. per square inch. The corresponding mean effective pressure for air is (0.0764/0.065) X 11.9 = 14.0, and the final pressure from Table 1 is 19.4 bl. per square inch gage. Suppose the nearest standard compressor is rated 16,000 en. ft. per minute, and 15 Ib. per square inch at 3,200 r.p.m. The mean effective pressure for 15 Ib. is 11.44 and for 19.4 is 14.0. The standard compressor must therefore be speeded up to 3,200 X VH/11.44 or 3,540 r.p.m. For a constant "load coefficient" Q/N, the new quantity will be 16,000 X 3,540/3,200 = 17,700. So if it is desired to use the standard compressor and save the extra cost of a special size, then only 17,700 cu. ft. per minute of the gas can be exhausted with a suction of 7 Ib. per square inch gage, or the compressor can be speeded up to handle 18,500 cu. ft. per minute, but the suction will be somewhat above 7 Ib. If the horsepower required by the standard compressor is 1,300 (corresponding to a shaft efficiency of 0.6.15) the horsepower for the desired conditions will be 1,300 X (17,700/16,000) X Ul.9/11.44) = 1,495.